LESSON 2.10 Understanding work, energy, power and efficiency.

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1 LESSON 2.10 Understanding work, energy, power and efficiency. Work(W),Enegy(E) and Power (P) and Effiecency Example 2 Figure shows an ice cube is pulled by a force 20N At an angle of 60 o to the surface of the smooth surface. (a) The Definition and S.I. unit of Work Work is defined as the product of the applied force,f on the object and its displacement,s in the direction of the net force. W = Fs where W = Work, F = force and s = displacement The S.I.unit for Work is Joule(J) I J = 1 N m Work is a scalar quantity. Example 3 Calculate the done on the ice cube? Figure shows a graph force-displacement of spring which is compressed by a force increases from 0 N to 100 N for 0.15 m. Work done also can get from the graph force-displacement. Calculate the work done on the spring. Example 1 A horse pulls a carriage with a total force 40 N for 50m. Calculate the work done on the carriage by the horse. (b) The Definition and S.I. unit of Energy(E) Energy is the capacity or ability of a system to do work. Without enegy the work cannot done. When work is done, energy is transferred to the object or change into a different form. Energy can exist in various form ; potential energy(gravitational Potential Energy, Elastic Potential Energy, Electrical Potential Energy, Atomic Potential Energy ) kinetic energy,mechanical energy, heat energy,sound energy, electrical energy and nuclear energy. 1

2 The S.I. of energy is Joule (J).Energy is scalar quantity. Example 4 A student lifts a brick of mass 0.8 kg from the floor to the table top of height 1.2 m.determine (a) work done on the brick (b) energy is used to lift the brick. Kinetic Energy ( E k ) Kinetic energy is the energy possessed by a moving object. E k = ½ mv 2 m = mass, v = velocity Example 5 A bullet of mass 0.02 kg moves at a velocity 150 ms -1 What is the kinetic energy of the bullet? Example 6 A ball of mass 0.2 kg is thrown to a height 15 m. How much gravitational potential energy does the ball gain? Example 8 A boy of mass 50 kg sitting on the top end of an inclined sliding board has an energy of 2 kj. What is the height the inclined sliding board from the ground? Principle of Conservation of Energy Energy cannot be created or destroyed. Energy can be transformed from one kind to another, but the total energy in a system stays the same or is conserved. Example 9 A stone is thrown with a velocity 20 ms -1. What is the maximum height can be reached by the stone? A moving lorry of mass 800 kg has an energy of 160 k J. What is the velocity of the lorry. Gravitational Potential Energy ( E g) The Gravitational potential energy of any object is the energy stored in the object because of its height above the earth s surface E g = m g h m = mass g = acceleration due to gravity h = height Example 7 Example 10 Figure shows a ball of mass 0.5 kg slides from rest at point A through a a frictionless rail height 0.8 m down. What is the velocity of the ball at the bottom of the rail. 2

3 Example 11 Figure shows a trolley is released from a rest at point X through a frictionless inclined plane. (c) The Definition and S.I. unit of Power (P) Power is the rate at which work is done or Power is the rate at which energy is changed or P = W or P = Fs = F v t P = E t What is the velocity of the trolley at point Y. P = Power, W = Work, E = Energy, t = time v = velocity The S.I. unit of power is Watt(W) 1 W = 1 Js-1 Example 13 A monkey of mass 20 kg climbs a coconut tree of height 15 m in 2.5 s. What is the power of the monkey? Example 12 Figure shows a ball moves on a frictionless curve track with a velocity 6 ms -1 at point A. (d) The Definition of Efficiency Efficiency = useful energy transferred x 100% total energy supplied Example 14 = useful energy output x 100% energy input What is the velocity of the ball when it reaches at point B? A man pulls a box of mass 8 kg with a total force 100 N. After pulled for 5 m,the box is moving at a speed of 6 ms -1. Calculate the efficiency with which the man is using his energy to pull the box. 3

4 Example 15 A crane lifts a load of 400 kg to a height of 100 m in 20 s. If the power input is W, calculate (a) the useful energy output (b) the energy input (c) the efficiency of the crane. (e) Appreciating the importance of maximising the efficiency of devices. Energy conservation demands that the total energy output of a machine or device must equal its energy input. However, when we measure the energy output as work done on the load by a machine or device, we find it is less than the energy input. It is because the machine or device also does work against frictional forces and sometimes does work in moving itself. The work done against friction converts input energy into wasted heat energy and a little noise energy. So the energy equation now looks like this: Energy = useful energy + wasted energy Input output output Maximising the efficiency of machine or device makes the best use of the input energy and reduces wasted energy output. Maximising the efficiency of machine and device can helps (a) to conserve resources since fossil fuels such as coal, petroleum and natural gas are non-renewable resources (b) to protect the enviroment from deforestation,oil spills and radioactive wastes (c) to reduce the emission of air pollutants and greenhouse gases from power stations (d) to reduce the energy bills The following are several ways of increasing the efficiency of machines and devices: Machines: Moving surfaces are made as smooth as Possible. Lubricants such as oil and silicone are used to separate surfaces. Rollers and ball bearings are used to separate rotating axles from their mountings. Cushions of air are used as elastic lubricant. Machines which move through fluids are made streamlined in shape to reduce the frictional drag. Heat engines: Heat engine must be designed with capability to do a greater amount of mechanical work while discharging waste heat at a lower temperature. Electrical devices: (i) Lamp: A fluorescent lamp is more efficience than a filament light bulb. Use a lamp with a reflector so that the illumination can directed to specific area. A lighting of a room should depend on the size of the room. (ii) Water heater When having a shower during a hot weather, a lower temperature is needed (iii) Refrigerator The doors of the refrigerator must always be shut tight. Thermostat should be used in refrigerator to control the temperature The power of refrigerator needed depend on the size of the family. Another ways: Recycling also conserves energy resources. Recycling saves energy because we do not have to make new bottles, papers e.t.c. 4

5 TUTORIAL Which of the following is true? A B C Work is a vector quantity Work and energy has the same unit Work is the product of force and distance 2 1 J is equivalent to A 1 kg m B 1 N s C 1 kg s D 1 N m 3 Choose the figure which shows the student doing the maximum work. What is the work done to lift the object to the top of the rough rail. A 40 J B 240 J C 320 J D 400 J E 560 m 6 An object of mass 4 kg moves at a velocity 2.5 ms -1. What is the kinetic energy of the object. A 5.0 J B 10.0 J C 12.5 J D 25.0 J E 30.0 J 7 A moving car of mass 800 kg has an energy of 250 k J. What is the velocity of the car. A 2 ms -1 B 10 ms -1 C 20 ms -1 D 25 ms -1 E 30 ms -1 8 The figure shows a student running up a staircase at a constant speed. 4 An object of mass 0.4 kg is pulled by a force of 20 N over a distance of 1.5 m on horizontal surface..the angle between the force to the horizontal surface is 60 o to the horizontal. What is the work done on the object. Which physical quantity increases while the student is running up the staircase? A 26 J B 20 J C 15 J D 10 J E 5 J 5 Figure shows an object of mass 1.5 kg lifted to the top of a rough rail with a force of 80 N. A B C D Inertia of the student Momentum of the student Kinetic energy of the student Gravitational potential energy of the student 5

6 9 A boy of weight of 500 N walking up a staircase consisting of 20 steps. Each step is 40 cm height. How much gravitational potential does he gain? Which one of the following graphs is true regarding the oscillation of the pendulum? A 40 J B 400 J C 4000 J D J E J 10 Which of the following is true regarding the Principle of Conservation of Energy A B C Energy can be created or destroyed Total energy in a system stays the same Energy cannot be transformed from one kind to another 11 Figure shows a pendulum oscillating between positions P and S. What is the position of the bob possess both of kinetic energy and gravitational potential enegy? 13 A moving lorry has kinetic energy. When the lorry stops,its kinetic energy is zero. This is because the kinetic energy A B C D is destroyed is used to stop the lorry converted to gravitational potential energy converted to heat energy as result of friction 14 The figure shows the path of a ball rolling down a smooth sloope. A P B Q C R D S 12 Figure shows a pendulum oscillating between positions X and Z. The ball has the greatest change in gravitational potential energy between A P and Q B Q and R C P and S D R and T 15 Figure shows a ball is released from a rest at point A of a frictionless track. 6

7 Which of the following is true? A The total of energy at all the points is same B The velocity of the ball at point A is same as the velocity of the ball at point C The kinetic energy of the ball at point B is same as the kinetic energy of the ball at point C D The gravitational potential energy of the ball at point A is same as the gravitational potential energy of the ball at point E A 5.0 m B 10.0 m C 20.0 m D 40.0 m E 60.0 m 19 Figure shows of a ball of mass 0.05 kg moves on a rough track with a velocity 6 ms -1. At height of h the velocity of the ball is 2 ms Figure shows a trolley is released from a rest at the top end of a frictionless curve track. What is the value of h? What is the velocity of the trolley when it reaches the bottom of the track? A 5 ms -1 B 7 ms -1 C 8 ms -1 D 9 ms -1 E 10 ms -1 A 0.9 m B 1.0 m C 1.2 m D 1.4 m E 1.6 m 20 Figure shows a trolley moves on a curve track with a velocity 8 ms -1 at point A. It reaches of a height of 1.95 m. 17 Figure shows a simple pendulum has a 150-g bob at the end of a string is released from a state of rest at point A. What is the velocity of the trolley at point B? Determine the velocity of the bob at the lowest point B. A 2 ms-1 B 3 ms-1 C 2 ms-1 D 3 ms-1 E 4 ms A tennis ball of mass 20.0 g is thrown vertically with a velocity of 20 ms -1. What is the maximum height reaches by the ball? A 5.0 ms -1 B 5.6 ms -1 C 6.4 ms -1 D 8.0 ms -1 E 9.2 ms A lift in a hotel can raise 8 people through a height of 20 m in 5 seconds. The lift plus passengers has a mass of 800 kg. What is the power of the lift motor? A 40 W B W C W D W E W 7

8 22 The figure shows a motor lifting a load of mass 8.0 kg. The motor takes 4.0 s to lift the load to a height 0.5 m. 26 Figure shows an electric motor on a buildingsite lifts a load of mass 2 kg top of a house. The house is 15 m high and it takes 7.5 s to lift the load. What is the power of the motor? A 4 W B 10 W C 16 W D 4 0 W E 160 W 23 A motor can raise a mass of 10 kg with a uniform velocity 20 ms -1. What is the power of the motor? A 2 W B 200 W C W D W E W 24 Figure shows a worker pulling a borrow up a ramp. (a) Determine the weight of the load. (b) What is the work to lift the load by the motor? (c) How much gravitational energy does the load gain? (d) Compare your answer in (b) and and give the reason.(c) (e) What is the power of the motor. What is the efficiency of the ramp? A 25 % B 40 % C 50 % D 75 % E 80 % 25 A pump lifts 200 kg water per minute through a vertical height of 15 m. Calculate the power input rating of the pump if it is 65% efficient? A 480 W B 500 W C 640 W D 770 W E 890 W 27 Figure shows two boys Ali and Abu of masses 42 kg and 60 kg respectively running up a staircase in a competation. They start running at the same time. Abu is announced as the winner of the competation. (a) Determine the work done by Abu. (b) What is the diffrerence in gravitational potential energy of Ali and Abu? 8

9 (c) Although Abu is the winner, the power of Ali is bigger than the power of Abu. Give the reason for your answer (d) (e) What is the acceleration of the athelete at the position P? Why is the thick mattress with a soft surface is used in this event. 28 Figure shows an athlete of mass 60 kg in a pole pole vaulting event. J, K,L,M,N,O,P and Q are the positions taken by the athlete. The height of the bar from ground is 5 m. The higest height reaches by the athlete from the bar is 0.2 m. 29 The figure shows smooth inclined track, PQ, and a rough surface QR is used to transfer a bag of cement into a lorry. The bag of cement of 50 kg mass is released from P at a height of 5 m and slides to Q and stops at R. (a) Explain why at the position K, the athelete accelerates at a specific speed before he starts to jump. (b) Why is the pole is bent at the position L?. (a) (i) Name the type of energy the bag of cement has at P. (ii) Calculate the energy in (a) (i). (c) Calculate the maximum gravitational potential energy of the athelete. (b) State the type of motion of the bag of cement along the track PQ. 9

10 (c) The bag of cement experiences an average frictional force of 100 N along QR and stops at R. (i) Calculate the velocity of the bag of cement at Q. 31 Each figure below shows two positions of a student on a swing. The initial position in each figure is different. (ii) Calculate the distance QR. (iii) State the changes of energy when the bag of cement moves from Q to R Figure shows a crane lifts a load of 800 kg to a height of 150 m in 20 s. The power input of the crane is 75 kw. (a) Determine (i) the useful energy output (iii) the energy input Observe the positions of each of the swing in each diagram and the appearance of the student when she swings. Based on the observations: (a) State one suitable inference that can be made. (b) State one apporopriate hypothesis for an investigation. (c) With the use of apparatus such as trolley, ticker timer and other apparatus, describe an experimental framework to test your hypothesis. In your description, state clearly the following: (i) Aim of the experiment (ii) Variables in the experiment (iii) List of apparatus and materials (iv) Arrangement of the apparatus (v) The procedure of the experiment which include the method of controlling the manipulated variable and the method of measuring the responding variable. (vi) Way you wouldttabulate the data (vii) Way you would analysis the data (iii) the efficiency of the crane (b) Compare your answer in (a)(i) and (a)(ii) and give your reason for your answer. 10